A Classical Trigonometric Identity. Or Not?

Geometry Level 2

12sinxcosx+sin22x+cos22xcos2x=sinxcosx+sinx\sqrt{1-2\sin x \cos x}+\sqrt{\sin^22x+\cos^22x-\cos^2x} \\ = \\ \left |\sin x-\cos x \right |+\left | \sin x \right | Is the above equation a trigonometric identity?

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